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A note on zeroes of real polynomials in  spaces
Author(s):
Jesús
Ferrer
Journal:
Proc. Amer. Math. Soc.
137
(2009),
573-577.
MSC (2000):
Primary 47H60, 46B26
Posted:
August 19, 2008
MathSciNet review:
2448577
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Abstract:
For real  spaces, we show that being injected in a Hilbert space is a 3-space property. As a consequence, we obtain that, when  does not carry a strictly positive Radon measure, every quadratic continuous homogeneous real-valued polynomial on  admits a linear zero subspace enjoying a property which implies non-separability.
References:
-
- 1.
- R.M. Aron, C. Boyd, R.A. Ryan, I. Zalduendo, Zeros of polynomials on Banach spaces: The real story, Positivity 7 (2003), pp. 285-295. MR 2017308 (2004j:46066)
- 2.
- T. Banakh, A. Plichko, A. Zagorodnyuk, Zeros of quadratic functionals on non-separable spaces, Colloq. Math. 100, No. 1 (2004), pp. 141-147. MR 2079354 (2005g:46047)
- 3.
- J. Ferrer, On the zero-set of real polynomials in non-separable Banach spaces, Publ. of R.I.M.S. 43, No. 3 (2007), pp. 685-697. MR 2361792
- 4.
- J. Ferrer, Zeroes of real polynomials on
 spaces, J. Math. Anal. Appl. 336 (2007), pp. 788-796. MR 2352980 - 5.
- N. J. Kalton, N. T. Peck, Twisted sums of sequence spaces and the three-space problem, Trans. Amer. Math. Soc. 255 (1979), pp. 1-30. MR 542869 (82g:46021)
- 6.
- H. P. Rosenthal, On injective Banach spaces and the spaces
 for finite measures  , Acta Math. 124 (1970), pp. 205-248. MR 0257721 (41:2370)
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Additional Information:
Jesús
Ferrer
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjasot (Valencia), Spain
Email:
Jesus.Ferrer@uv.es
DOI:
10.1090/S0002-9939-08-09574-9
PII:
S 0002-9939(08)09574-9
Keywords:
Quadratic polynomials,
zero-set,
$C(K)$ spaces
Received by editor(s):
January 23, 2008
Posted:
August 19, 2008
Additional Notes:
The author has been partially supported by MEC and FEDER Project MTM2005-08210
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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